Development and Validation of a Novel Bird Strike Resistant Composite Leading Edge Structure

A novel design of a fibre-reinforced composite Leading Edge (LE) of a Horizontal Tail Plain (HTP) is proposed. The development and validation approach of the innovative composite LE structure are described. The main design goal is the satisfactory impact resistance of the novel composite LE in the case of bird strike. The design concept is based on the absorption of the major portion of the bird kinetic energy by the composite skins, in order to protect the ribs and the inner LE structure from damaging, thus preserving the tail plane functionality for safe landing. To this purpose, the LE skin is fabricated from specially designed composite panels, so called ‘tensor skin’ panels, comprising folded layers, which unfold under the impact load and increase the energy absorption capability of the LE. A numerical model simulating the bird strike process is developed and bird strike experimental testing is performed, in order to validate the proposed layout and prove the capability of the structure to successfully withstand the impact loading. The numerical modelling issues and the critical parameters of the simulation are discussed. The present work is part of the European Aeronautics Research Project, ‘Crashworthiness of aircraft for high velocity impact – CRAHVI’ [1].     

A numerical method for analysis of bounded metalworking processes

This paper describes a numerical procedure for the solution of metalworking problems of a strain-hardening material. The overall metalworking process is split up into a number of stages and the governing equations for a typical stage are set up in terms of incremental displacements. The incremental deformation occurring in each successive stage is found by an interative numerical procedure based on the concept of piecewise linearization. The ‘composite’ solution yields the distribution of stress and strain in the work material at various stages of the process. Finally, application of the method to finite axisymmetric compression is described.     

A study on fiber orientation influence on the mechanical response of a short fiber composite structure

This paper deals with the structural analysis of composite materials with non-homogenous orientation of the reinforcement. During this research, a short fiber-reinforced polymer matrix composite is studied. In this case, inhomogeneity of the reinforcement orientation caused by injection molding manufacturing process is analyzed. The main objective of the paper is the investigation of an influence of process-induced orientation of the reinforcement on mechanical properties of the material in comparison with unidirectional and random reinforcement orientation. In particular, natural frequencies and transient response of an exemplary composite component are investigated. To specify effective properties of the composite, Mori–Tanaka’s micromechanical model is assumed. Orientation distribution of the reinforcement is determined by injection molding simulation. To determine elastic material properties dependent on non-homogenous orientation of the reinforcement, an orientation averaging procedure is taken into account. Therefore, during this study, effectiveness of the orientation averaging procedure and different closure approximations influence on the results are studied. Orientation averaging results are compared with numerical results obtained by finite element-based homogenization of composites with prescribed second-order orientation tensor. Finally, the obtained material parameters were applied into a macroscale finite element model, and numerical simulation with different boundary conditions was conducted.     

Simulation of light‐weight membrane structures by wrinkling model

The computational challenge in dealing with membrane systems is closely connected to the lack of bending stiffness that constitutes the main feature of this category of structures. This manifests numerically in badly conditioned or singular systems requiring the use of stabilized solution procedures, in our case of a ‘pseudo‐dynamic’ approach. The absence of the flexural stiffness makes the membrane very prone to local instabilities which manifest physically in the formation of little ‘waves’ in ‘compressed’ areas. Current work presents an efficient, sub‐iteration free ‘explicit’, penalty material based, wrinkling simulation procedure suitable for the solution of ‘static’ problems. The procedure is stabilized by taking full advantage of the pseudo‐dynamic solution strategy, which allows to retain the elemental quadratic convergence properties inside the single solution step. Results are validated by comparison with published results and by setting up ‘numerical experiments’ based on the solution of test cases using dense meshes. Copyright © 2005 John Wiley & Sons, Ltd.     

纤维增强复合材料三明治板破片穿甲数值仿真

研究破片对（由钢板、纤维增强复合材料板及钢板叠合而成）纤维增强复合材料三明治板穿甲过程中能量转化规律。进行破片模拟弹丸(FSP)对不同结构三明治板高速穿甲数值仿真,获得FSP破片对16种三明治板的弹道极限,并与实验结果对比验证数值仿真的可信度。通过分析数值仿真结果,进一步研究破片临界贯穿条件下纤维增强复合材料三明治板各组成部分吸能比率与结构尺寸相关性。结果表明,不同厚度夹层板的吸能比率恒定(芳纶纤维10.41%,玻璃纤维2.68%),夹层板内能随厚度的增加呈二次函数增加。由此获得破片对纤维增强复合材料三明治板弹道极限速度计算方法。     

Numerical modeling on pultrusion of composite I beam

Pultrusion is one of the most efficient methods for making fiber reinforced polymer composite parts. However, more work needs to be done to develop scientific means for the pultrusion tooling design and process control. This paper describes numerical simulation on the pultrusion of fiberglass–vinyl ester composite I beams using a numerical procedure based on general-purpose FE packages. The theory and numerical implementation of the procedure is briefly introduced. The procedure is verified by good agreement between the predicted temperature profiles and the experimental ones. The effect of various process parameters and/or heating configurations on the temperature and curing profiles in the composite I beams are investigated numerically. The results are used to determine preferred process conditions and/or heating configurations for the pultrusion of the composite I beams.     

A Study on Skin Delaminations Growth in Stiffened Composite Panels by a Novel Numerical Approach

In this paper, a study on skin delamination growth in stiffened composite panels made of carbon fibres reinforced polymers and subjected to compressive load is presented. A robust (mesh and time step independent) numerical finite elements procedure, based on the Virtual Crack Closure Technique (VCCT) and on the fail release approach, is used here to investigate the influence of skin delamination size and position on the damage tolerance of stiffened composite panels. Four stiffened panels configurations with skin delaminations differently sized and positioned are introduced. Bay delaminations and delaminations under the stringer foot are considered. The novel numerical procedure has been used to simulate the delamination growth for all the investigated panel configurations and to evaluate the influence of the delaminations’ geometrical parameters on the growth development. As a confirmation of the applicability and effectiveness of the adopted numerical tool, the numerical results, obtained for all the analysed configurations, in terms of grown delaminated area, displacements and strains measured in various panel locations, have been compared with experimental data available in literature.     

复合材料层合板分层损伤数值模拟方法研究现状

复合材料层合板在航空航天等领域受到广泛应用,分层损伤作为复合材料层合板主要的损伤形式,对复合材料结构的强度和刚度有显著的影响,是限制其重大工程应用的热点问题之一。通过实验的方法对复合材料结构进行研究,往往需要耗费大量的时间和成本,成熟的有限元数值模拟技术可以较低成本实现复合材料结构的分层行为模拟,成为分层损伤研究的重要手段。本文从数值模拟角度总结了国内外在纤维增强复合材料分层损伤取得的研究成果,并对目前主要的方法虚拟裂纹闭合技术(VCCT)、内聚力模型(CZM)及扩展有限元法(XFEM)进行阐述。最后,对其发展方向进行了展望。      

Comparison of several closure approximations for evaluating the thermoelastic properties of an injection molded short-fiber composite

The accurate prediction of both the elastic properties and the thermal expansion coefficients is very important for the precise simulation of such processes as injection molding of short-fiber polymer–matrix composites. In this work, a two-step homogenization procedure is applied and compared with experimental values obtained on a polyarylamide/glass fiber composite for a broad range of temperatures. It is observed that the stiffness averaging version of the model surpasses the compliance averaging variant, especially when it is combined with a precise evaluation of the fourth-order orientation tensor. It is also demonstrated that the orthotropic closure approximations are significantly better than previous ones (linear, quadratic, and hybrid) and than a very recent one. Among the orthotropic closure approximations, the fitted ones lead to acceptable results, which are very close to those obtained with the experimentally measured fourth-order orientation tensor.     

Hyperelastic large deformations of two-phase composites with membrane-type interface

The composite under investigation consists of two phases which are bonded together through a membrane-type interface. The work reported in this paper aims at studying the hyperelastic large deformations of this composite while accounting for interfacial stress effects. A variational formulation for a general traction boundary value problem of the composite is provided, leading to the local bulk and interfacial equilibrium equations and to the traction boundary conditions. Assuming that each bulk phase is incompressible and characterized by an energy density function depending only on the trace of the right Cauchy-Green bulk strain tensor and that the interface is compressible and defined by an energy density function being isotropic with respect to the right Cauchy-Green surface strain tensor, exact solutions are given for the simple axial extension, simple torsion and out-of-plane shear of a fiber-reinforced cylinder, and a closed-form solution is also found for a hollow composite sphere subjected both to an internal pressure and an external pressure. These analytical results are further specified and discussed in the particular case where each bulk phase is described by an incompressible Neo-Hookean law and the interface is specified by a compressible Neo-Hookean law. Apart from their own usefulness, the results obtained in this work can serve as benchmarks for relevant numerical methods.     

An anisotropic linear elastic boundary element formulation for masonry wall analysis

This work presents an application of a Boundary Element Method (BEM) formulation for anisotropic body analysis using isotropic fundamental solution. The anisotropy is considered by expressing a residual elastic tensor as the difference of the anisotropic and isotropic elastic tensors. Internal variables and cell discretization of the domain are considered. Masonry is a composite material consisting of bricks (masonry units), mortar and the bond between them and it is necessary to take account of anisotropy in this type of structure. The paper presents the formulation, the elastic tensor of the anisotropic medium properties and the algebraic procedure. Two examples are shown to validate the formulation and good agreement was obtained when comparing analytical and numerical results. Two further examples in which masonry walls were simulated, are used to demonstrate that the presented formulation shows close agreement between BE numerical results and different Finite Element (FE) models.     

An investigation into the mixed-mode delamination growth in unidirectional T800/924C laminates

This study presents the results of experimental investigations and numerical simulation on mixed-mode I/II delamination growth initiated from an artificial transverse notch. Specimens made of unidirectional carbon fiber epoxy (T800/924C) composite have been tested under three-point-bend condition. A finite element procedure has been introduced to model 3-D stable delamination growth in the specimen to generate numerical growth data including loads, displacements, delamination lengths, and the growing crack front shapes. The simulation method uses strain energy release rate criterion in conjunction with a moving mesh facility. It is shown that very good compatibility exists between experimental and numerical results. A finite element-based data reduction method is then described as an application of the simulation procedure. Based on the obtained results, it is stated that this bending specimen can effectively be used in practice to study the mixed-mode crack growth and to measure interlaminar fracture toughness of unidirectional laminates.     

Finite element calculation of 4-step 3-dimensional braided composite under ballistic perforation

The ballistic perforation test results of 4-step 3-dimensional (3D) braided Twaron^®/epoxy composites, which were subjected to impact by conically cylindrical steel projectile, are presented. The residual velocities of projectile perforated composites target at various strike velocities were measured and also compared with that from finite element calculation. ‘Fiber inclination model’ for 3D textile composites was adopted to decompose the 3D braided composite at quasi-microstructure level for the geometrical modeling in preprocessor of FEM. The material modeling was also based on this simplified model. The finite element code of Ls-Dyna was used to simulate the impact interaction between projectile and inclined lamina. The residual velocity of projectile perforating the entire 3D braided composite can be calculated from the sum of kinetic energy loss of the projectile that obtained from FEM. From the simulation of ballistic penetration process and comparison between numerical results and experimental results, it proves that the analysis scheme of quasi-microstructure level in this paper is valid and reasonable. The simplified method in this paper could be extended to model other kinds of 3D textile composites under ballistic impact.     

Development of experimental,theoretical and numerical tools for studying thermo-oxidation of CFRP composites

In our laboratory, recent studies concerning damage mechanisms of continuous carbon/epoxy composites induced by isothermal ageing or thermal cycling have shown interactions between mechanical loading and oxidation process. The objectives of the research program named COMEDI, initiated at LMPM-ENSMA, in collaboration with CCR-EADS, LIM ENSAM and supported by the – French – Research National Agency ANR, are to better understand these couplings and to develop a numerical tool capable to predict the evolution of the mechanical behavior of a composite laminate subjected to a thermal ageing. In this paper, on one hand the expression of the interactions between mechanics, oxygen diffusion and chemical reaction will be deduced from thermodynamics concepts for a neat resin material. On the other hand, interest will be put on the development of a ‘user’ finite element involving the first disposable couplings: matrix shrinkage and evolution of the elastic modulus with oxidation. An application will be presented in the case of a unidirectional CFRP composite model, which gives the stress field around carbon fibers induced by the oxidation of the matrix. At last, a specific experimental device developed at the laboratory will be presented. This heated and pressurized vessel will allow performing accelerated thermal aging tests of samples submitted to constant deformation in order to put coupling effects under evidence, as well as to improve and validate the modeling approach.     

A study of fiber orientation in short fiber-reinforced composites with simultaneous mold filling and phase change effects

Most of the properties of injection molded short fiber-reinforced composites are highly dependent on the patterns of their fiber orientation, which are induced by the flow. On the other hand, in most practical injection molding processes, both filling and solidification of the molten suspension takes place simultaneously. This behavior indicates that both filling and phase change for solidification can occur at the same time and therefore affect the flow behavior of the suspension, hence the fiber orientation. The aim of the current work is to present a numerical analysis of fiber orientation prediction in a three-dimensional rectangular cavity considering simultaneous mold filling and phase change of the suspending polymer. To trace the flow front during the filling process, the volume of fluid method (VOF) has been used, while an enthalpy-based approach was used to model the solidification. The standard Hybrid closure model of Advani and Tucker was applied to approximate the evolved fourth order orientation tensor during the fiber orientation calculation. To validate the developed numerical model, the results of the simulation model were compared with available experimental data for the rectangular cavity. The simulation results showed that they are in good agreement with the experimental data. Hence, the numerical model could assist in decisions regarding the design of polymer composite products.     

Progressive failure analysis of 2/2 twill weave fabric composites with moulded-in circular hole

Micromechanical three-dimensional finite element models of 2/2 twill weave T300 carbon/epoxy woven fabric composite panels with moulded-in circular hole are established for stress analysis. In these models, the streamline equation is used as a shape function to simulate the fibre configuration. A progressive failure analysis together with a newly developed ‘maximum notched strength method’ are also proposed to predict the failure modes and notched strengths of the fibre dominated laminate with moulded-in hole. Perforated specimens of different hole sizes are prepared using a special procedure. Tension tests are performed to evaluate the stress–strain and failure characteristics. An increase in tensile strength with increasing hole size is observed within the experimental data range. Numerical results from progressive failure analysis provide good prediction to the failure phenomena of the fractured specimens. The notched strengths from the proposed numerical procedure are slightly higher than the experimental results.     

Numerical model for composite structures with experimental confirmation

The paper briefly presents a numerical model for the simulation of composite structures. The main structure is modeled with two‐dimensional plane finite elements. The composite surface is modeled with two‐dimensional interface elements for the continuous connection simulation and modified beam elements for the discrete connection simulation. The applied material model’s primary purpose is the simulation of reinforced concrete structures. It includes the most important nonlinear effects of reinforced concrete behavior: yielding in compression and opening and propagation of cracks in tension, with tensile and shear stiffness of cracked concrete, as well as the nonlinear behavior of reinforced steel. It also includes nonlinear behavior of the composite surface and the connection elements. The model was confirmed in experimental tests of composite concrete Omnia slabs, which are in common usage. The achieved test results were compared with the results obtained through the developed numerical model.     

Symmetric Galerkin boundary integral formulation for interface and multi-zone problems

Domains containing an ‘internal boundary’, such as a bi-material interface, arise in many applications, e.g. composite materials and geophysical simulations. This paper presents a symmetric Galerkin boundary integral method for this important class of problems. In this situation, the physical quantities are known to satisfy continuity conditions across the interface, but no boundary conditions are specified. The algorithm described herein achieves a symmetric matrix of reduced size. Moreover, the symmetry can also be invoked to lessen the numerical work involved in constructing the system of equations, and thus the method is computationally very efficient. A prototype numerical example, with several variations in the boundary conditions and material properties, is employed to validate the formulation and corresponding numerical procedure. The boundary element results are compared with analytical solutions and with numerical results obtained with the finite element method. © 1997 John Wiley & Sons, Ltd.     

Characterization of fiber orientation in short fiber reinforced composites with an image processing technique

An experimental method is developed to measure the three-dimensional fiber orientation in short fiber reinforced composites by utilizing an image processing technique. The second order orientation tensor can be calculated with geometrical data that were obtained from two parallel planar cross-sections. The orientation state of individual fibers is determined from the geometry of the elliptical cross-sectional shape on the polished surface. The basic concept in determining the three-dimensional fiber orientation tensor is to slice the composite sample twice in the same direction within a small distance. The tensor is determined by using a digital image processing technique and a computational code which calculates the tensor from the geometrical characteristics obtained for the elliptical fiber cross-sections. Experiments are performed to measure the three-dimensional orientation tensor of composite specimens and good results are obtained by using the method proposed in this study Electronic Publication